The Celtics have three advantages over the Heat head to head IMO:
1. Great teams can beat great stars, when the team is firing on all cylinders and the team is not. Think 2004 Pistons vs Lakers.
2. The Celtics can matchup with Wade / Allen and especially Bosh / KG and use man D to take away a lot of what that player does, without having to help. (West and Rondo can take Wade too. Although West is not the offensive threat Allen is.) They also have a bit of an "in your head" thing with Lebron, but I think that's over rated.
3. The Celtics still have a deep cast of guys who, while not super stars every night can go "superstar" in a game or a series. My list of guys who can look like super stars: Rondo, Ray, Pierce, KG, Shaq, BBD, Nate. Really the heat have Wade / Bosh / Lebron who can go super star and maybe Miller.
I think the Heat stats will say the Heat are better at end of rgular season (90%) chance, and probably 75% chance they have a better record than C's. But the gap is not so huge that the C's cannot hope to beat the Heat, and especially the C's advantages outlined above, I think its more like 50/50 who would win the series.
(Caveat: assumes health and even officiating in a 7 game series.)